Yes, but timber merchants rather than sheds or BMs. You're more likely to find it in a posh area where big front doors are the norm
For exterior, probably not a good idea. The smaller the section, the quicker it rots
Very expensive for one door, and you're not trying to match anything exactly.
Doesn't matter what the moulding is called. Sounds like depth is the key dimension for you, so just look for something close.